States of Linear Systems, Automata, and Marriage : A Tribute to Rudolf Kalman [Historical Perspectives]

During my time as a Ph.D. student in mathematics at the Massachusetts Institute of Technology (MIT), around 1962 or 1963, the authors of a book on control theory [1] introduced me to two researchers at MIT's Lincoln Laboratory, Michael Athanassiades and Peter Falb, who were writing a book on mathematical control theory. They, in turn, provided me with a draft of their book in progress and introduced me to the work of Rudolf Kalman. I read their draft with great interest not only for its intrinsic merit but also because I had been inspired by Norbert Wiener's Cybernetics and studied the Wiener-Hopf filter (and been a student of Wiener's at MIT for a while). Moreover, Kalman's stress on current state rather than the infinite past history of the system whose behavior was being extrapolated chimed with another of my interests, namely automata theory. There the concept of state was paramount-but in the world of sets and functions rather than vector spaces and linear transformations.